{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Copyright (C) 2016 - 2019 Pinard Liu(liujianping-ok@163.com)\n",
    "\n",
    "https://www.cnblogs.com/pinard\n",
    "\n",
    "Permission given to modify the code as long as you keep this declaration at the top\n",
    "\n",
    "MCMC(三)MCMC采样和M-H采样 https://www.cnblogs.com/pinard/p/6638955.html\n",
    "MCMC(四)Gibbs采样 https://www.cnblogs.com/pinard/p/6645766.html"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import random\n",
    "import math\n",
    "from scipy.stats import norm\n",
    "import matplotlib.pyplot as plt\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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S4jhCL6NR6moqWSXlkTDuvhZY22HbwwnP99C+KiluP3Buqp8v2WXy5MmEu+EmQqNp3EKg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\nCEoGIiKCkoGIiAD/Hw9Z0g2yGzJQAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x118bd710>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "def norm_dist_prob(theta):\n",
    "    y = norm.pdf(theta, loc=3, scale=2)\n",
    "    return y\n",
    "\n",
    "T = 5000\n",
    "pi = [0 for i in range(T)]\n",
    "sigma = 1\n",
    "t = 0\n",
    "while t < T-1:\n",
    "    t = t + 1\n",
    "    pi_star = norm.rvs(loc=theta[t - 1], scale=sigma, size=1, random_state=None)\n",
    "    #print theta_star\n",
    "    alpha = min(1, (norm_dist_prob(pi_star[0]) / norm_dist_prob(pi[t - 1])))\n",
    "\n",
    "    u = random.uniform(0, 1)\n",
    "    if u < alpha:\n",
    "        pi[t] = pi_star[0]\n",
    "    else:\n",
    "        pi[t] = pi[t - 1]\n",
    "\n",
    "\n",
    "plt.scatter(pi, norm.pdf(pi, loc=3, scale=2))\n",
    "num_bins = 50\n",
    "plt.hist(pi, num_bins, normed=1, facecolor='red', alpha=0.7)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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SMdSBZ0dHGf7kJ6eXHRur6xr+49AZ8rhEYXlHeHBwsK76VcM+Ik5JWg1sAXqADRGxW9Kq\n5PwQcB/wduAhSQATEbFkprp1tc6skuPHGejrO+vwsifPHmr44egoAytXnnW80h8GmPmPg7UXL1FY\nv8w1aCNiE7Cp7NhQavsu4K5a65rNp/NOnqz5D4NZN/MTtGZmOeCwNzPLgcxhHLNWqvRB6rOjo1Bh\naMbMZuawt/ZW4cNYj7eb1c/DOGZmOeCwNzPLAYe9mVkOOOzNzHLAH9CapVR84tZTKFgXcNibpVR6\n4tZTKFg38DCOmVkOuGdvbaHaTJZ+gMqscQ57aw91zGQ532aaOdNj+dZJHPZmGWaaOdNj+dZJPGZv\nZpYD7tmbGTB9gXHwIuPdJrNnL6lf0h5JeyWtrXD+KklPSToh6Ytl58YkPSfpGUmjzWy4mTXX5ALj\nk18nT59sdZOsiar27CX1AOuBWygtIL5D0kjZ8oI/B+4BllW4RACFiHipSe01M7NZyOrZLwH2RcRY\nREwAG4Gl6QIRcSwidgITM1xDjTfTzMwakTVmvwg4kNo/CNxYx/UD2CbpNDAUEV+vs33WhbwgiTXT\n6NOjrFyzEoAF5y1g3f2+HbaSrLCPBq9/c0QclnQpsFXSnojYXl5oYGBgartQKFAoFBp8WWtrXpDE\nmuikTk59kDw2PNbStsylYrFIsVicdf2ssB8HelP7vZR69zWJiMPJ92OSHqc0LFQ17M06hSdNs/lU\n3hEeHBysq35W2O8EFkvqAw4By4EVM5SdNjYv6QKgJyJek3QhcCtQX+vM2pgnTbNOUjXsI+KUpNXA\nFqAH2BARuyWtSs4PSVoI7ADeCpyR9AXgGuBfAI9JmnydRyLiibn7UczMbCaZD1VFxCZgU9mxodT2\nEaYP9Ux6Hbi+0QaamVnjPF2CmVkOOOzNzHLAc+PYnPEc9Wbtw2Fvc6eN56g3yxsP45iZ5YDD3sws\nBxz2ZmY54DF7sybyerXWrhz2Zk3k9WqtXXkYx8wsB9yzN8ux9LqzXnO2uznsrWF+eKpzTa47C/Dk\nqJ9/6GYOe2ucH54ya3sOezPrGl6icGYOezPrGnlZonA2fDeOmVkOZIa9pH5JeyTtlbS2wvmrJD0l\n6YSkL9ZT18zM5kfVYRxJPcB64BZKi4/vkDQSEbtTxX4O3AMsm0Vds1zwk7XWallj9kuAfRExBiBp\nI7AUmArsiDgGHJP0e/XWNcsLP1lrrZY1jLMIOJDaP5gcq0Ujdc3MrImyevbRwLVrrjswMDC1XSgU\nKBQKDbysmVn3KRaLFIvFWdfPCvtxoDe130uph16Lmuumw97MzM5W3hEeHBysq35W2O8EFkvqAw4B\ny4EVM5RVA3WtQ1SaGsHTInQWz4eTT1XDPiJOSVoNbAF6gA0RsVvSquT8kKSFwA7grcAZSV8AromI\n1yvVncsfxuZBhakRPC1CZ/F8OPmU+QRtRGwCNpUdG0ptH2H6cE3VumZmNv/8BK2ZWQ447M3McsBh\nb2aWA5710qyFKk6j4CkUmsLTHU/nsDdroUrTKHgKhebwdMfTeRjHzCwHHPZmZjngsDczywGP2VtF\nlaZFAE+NYNapHPZWWYVpEcBTI5h1Kg/jmJnlgMPezCwHPIxj1mbmYr1aT2tsDnuzNjMX69XmfVpj\nP03rsDe8IIl1Pz9N67A38IIkZjmQ+QGtpH5JeyTtlbR2hjJfTc7vkvT+1PExSc9JekbSaDMbbmZm\ntavas5fUA6wHbqG0gPgOSSPp5QUlfRR4b0QslnQj8BBwU3I6gEJEvDQnrTczs5pkDeMsAfZFxBiA\npI3AUiC9luzHgG8ARMTTkhZIuiwijibnyxciN7NZ8HTI1oissF8EHEjtHwRurKHMIuAopZ79Nkmn\ngaGI+HpjzTXLL0+HbI3ICvuo8Toz9d7/VUQcknQpsFXSnojYXl5oYGBgartQKFAoFGp8WTObie+t\n7y7FYpFisTjr+llhPw70pvZ7KfXcq5W5PDlGRBxKvh+T9DilYaGqYW9zx5Ob5Uve763vNuUd4cHB\nwbrqZ4X9TmCxpD7gELAcWFFWZgRYDWyUdBNwPCKOSroA6ImI1yRdCNwK1Nc6ay5PbmaWW1XDPiJO\nSVoNbAF6gA0RsVvSquT8UER8T9JHJe0D3gDuSKovBB6TNPk6j0TEE3P1g5iZ2cwyH6qKiE3AprJj\nQ2X7qyvU2w9c32gDzcyscX6C1qyDVZs0zSrL6zw5DnuzDlZ10jTnfUV5nSfH89mbmeWAe/ZdyLdY\nmlk5h3038i2WubV522ZOnDrBk6++zqFfPdcPUtkUh71ZFzlx6gQLrlrAy38/Ts+xEzx7/zAA5+89\nyrP3D3PiovNa3ML2kqcPax32Zl3owlOnuf28t3DtwtKntM8l2+uOnD28l2d5+rDWYd/hvMqUmdXC\nYd/pvMqUmdXAYW/W4SY/lAUYPzTOgqt8g72dzWFv1uEmP5QFeHH8xaplD+we5/w3p39w+8P1m7lp\ndf+ct7PddfuHtQ77DuF7560ZKn1w+39eP9HiVrWHbv+w1mHfKXzvvJk1wGFv1oEmx+mPHjvK+MlX\nGhqnP7B7HO4fnroXf9LEC8ea0VRrEw77NuTbKS3L5Dj9Ww68hdNxuqFrXXjqNGsWLpi6F3/SPT86\n02gzO1Y3jt9nhr2kfmAdpcVLHo6IByqU+SrwEeBNYGVEPFNrXavAt1NaG3jz9fw+gduN4/dVw15S\nD7AeuIXSurI7JI1ExO5UmY8C742IxZJuBB4Cbqqlbt7NxYeuxbGxxhpl07TT7/PYPx9jeHMpfOfj\nFsuLzwRrmvgE7tizY01qmc1GVs9+CbAvIsYAJG0ElgLpwP4Y8A2AiHha0gJJC4EraqibC9VCffiT\nnzzreCO9+HYKp27Q6t9n+h76N0+8WfMtlnOl0q2btfb4OzXsu2VIJyvsFwEHUvsHgRtrKLMIeFcN\ndbvOTOPtzQ51y4f0PfTxTLS4NTPPufPFv/9xxT8CL+w7wvmvvMGz9w9zJNnutPv600M6j37p0Y4N\n/qywr/XdpUYbUqvvfPvb/GjnzrOOX3X11dz2qU/NyWtWCvAf7trFTdddd1bZSsHuUM+XF154gf0v\n7J/av/bXr61YbvO2zRw9dpThzcMcOXSEhe9aCMCLB1+c1+GaZpjpj8B9z7/IHyTb/+PIcW745Um+\nseP/8WzZ3T/n7z3K43f9BVe8d+G04+12R9BMwQ+wa+curvuX15213S5/FBQxc55LugkYiIj+ZP9L\nwJn0B62S/gIoRsTGZH8P8FuUhnGq1k2Ot767YmbWgSKi5o52Vs9+J7BYUh9wCFgOrCgrMwKsBjYm\nfxyOR8RRST+voW5djTUzs9mpGvYRcUrSamALpdsnN0TEbkmrkvNDEfE9SR+VtA94A7ijWt25/GHM\nzKyyqsM4ZmbWHX6lVS8s6d9I+rGk05JuKDv3JUl7Je2RdGur2tipJA1IOijpmeSrc259aBOS+pP3\n315Ja1vdnk4naUzSc8n7cbTV7ek0kv5S0lFJz6eOvUPSVkk/lfSEpKqf5Lcs7IHngY8D/5A+KOka\nSuP71wD9wH+X1Mp2dqIA/nNEvD/52tzqBnWS1AOB/ZTehyskXd3aVnW8AArJ+3FJqxvTgf6K0vsx\n7V5ga0S8D/i7ZH9GLQvRiNgTET+tcGop8M2ImEgeyNpH6eEuq48/+J69qYcJI2ICmHwg0Brj9+Qs\nRcR24OWyw1MPtCbfl1W7Rjv2mN9F6QGsSZMPaVl97pG0S9KGrH/e2VlmelDQZi+AbZJ2Srq71Y3p\nEpdFxNFk+yhwWbXCczrrpaStwMIKp/59RHynjkv5U+QyVX63f0RpfqKvJPt/DPwZcOc8Na0b+P3W\nfDdHxGFJlwJbJe1JeqvWBBERWc8szWnYR8SHZ1FtHOhN7V+eHLOUWn+3kh4G6vnDame/B3uZ/q9N\nq1NEHE6+H5P0OKWhMod9Y45KWhgRRyS9E/inaoXbZRgnPZY3Atwm6VxJVwCLAX96X4fkP/ykj1P6\nMNxqN/UwoaRzKd0wMNLiNnUsSRdIujjZvhC4Fb8nm2EEuD3Zvh0YrlK2dYuXSPo48FXgEuB/S3om\nIj4SET+R9CjwE+AU8IfhhwHq9YCk6ykNR7wArGpxezqKHwhsusuAxyVBKXMeiYgnWtukziLpm5Sm\noblE0gHgPuB+4FFJdwJjwNmzLaav4Rw1M+t+7TKMY2Zmc8hhb2aWAw57M7MccNibmeWAw97MLAcc\n9mZmOeCwNzPLAYe9mVkO/H+JfIbMePMDYgAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x11c31970>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from mpl_toolkits.mplot3d import Axes3D\n",
    "from scipy.stats import multivariate_normal\n",
    "samplesource = multivariate_normal(mean=[5,-1], cov=[[1,0.5],[0.5,2]])\n",
    "\n",
    "def p_ygivenx(x, m1, m2, s1, s2):\n",
    "    return (random.normalvariate(m2 + rho * s2 / s1 * (x - m1), math.sqrt(1 - rho ** 2) * s2))\n",
    "\n",
    "def p_xgiveny(y, m1, m2, s1, s2):\n",
    "    return (random.normalvariate(m1 + rho * s1 / s2 * (y - m2), math.sqrt(1 - rho ** 2) * s1))\n",
    "\n",
    "N = 5000\n",
    "K = 20\n",
    "x_res = []\n",
    "y_res = []\n",
    "z_res = []\n",
    "m1 = 5\n",
    "m2 = -1\n",
    "s1 = 1\n",
    "s2 = 2\n",
    "\n",
    "rho = 0.5\n",
    "y = m2\n",
    "\n",
    "for i in xrange(N):\n",
    "    for j in xrange(K):\n",
    "        x = p_xgiveny(y, m1, m2, s1, s2)\n",
    "        y = p_ygivenx(x, m1, m2, s1, s2)\n",
    "        z = samplesource.pdf([x,y])\n",
    "        x_res.append(x)\n",
    "        y_res.append(y)\n",
    "        z_res.append(z)\n",
    "\n",
    "num_bins = 50\n",
    "plt.hist(x_res, num_bins, normed=1, facecolor='green', alpha=0.5)\n",
    "plt.hist(y_res, num_bins, normed=1, facecolor='red', alpha=0.5)\n",
    "plt.title('Histogram')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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CwSCGYRCJRKq/sQSi0WgBuTkpKxgaGqK9vd2WgUYZYyKRSD5CdeoSU0n3SCRS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\nQoCfQCTRt5H8Xitihvk2Io/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9jhUrIjz2mMHSpU/ZJj/DMHjzzTf54x+XsX59B9DDpEnz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\nPhMmTJgw8f8bUQAAJQuPgH3ohFMAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x11933550>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = plt.figure()\n",
    "ax = Axes3D(fig, rect=[0, 0, 1, 1], elev=30, azim=20)\n",
    "ax.scatter(x_res, y_res, z_res,marker='o')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.6.4"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 1
}
